In Young's double slit experiment, the separation between two slits is \(0.3 \times 10^{-3} \mathrm{~m}\). When light beam is passed through the two slits, then interference pattern is observed on the screen 1.5 m away. If the first violet and red fringes are formed 2.0 mm and 3.5 mm away from the central white fringe, then the difference in wavelength of red and violet light is \(x \times 10^{-9} \mathrm{~m}\). The value of \(x\) is

The electric force between two point charges separated by a certain distance in air is \(F\). The distance at which they should be placed in a
medium of relative permittivity \(k\), so that the force remains the same, is

Two slabs are of the thicknesses \(d_1\) and \(d_2\). Their thermal conductivities are \(K_1\) and \(K_2\), respectively. They are in series. The free ends of the combination of these two slabs are kept at temperatures \(\theta_1\) and \(\theta_2\). Assume \(\theta_1 > \theta_2\). The temperature \(\theta\) of their common junction is

In the expression \(\mathrm{P}=\mathrm{El}^2 \mathrm{~m}^{-5} \mathrm{G}^{-2}\) where \(\mathrm{E}, 1, \mathrm{~m}\) and G represent Energy, Angular Momentum, Mass and Gravitational Constant, the dimensions of P are

A source of sound gives 5 beats per second, when sounded with another source of frequency \(100 \mathrm{~s}^{-1}\). The second harmonic of the source, together with a source of frequency \(205 \mathrm{~s}^{-1}\) gives 5 beats per second. What is frequency of the source?

The potential energies associated with four orientations of an electric dipole in an electric field are
(i) \(-5 U_{0}\)
(ii) \(-7 U_{0}\)
(iii) \(3 U_{0}\)
(iv) \(5 U_{0}\)
where \(U_{0}\) is positive. Rank the orientations according to the angle between the electric dipole moment \(\mathbf{p}\) and electric field \(\mathbf{E}\), greatest first

A diffraction pattern due to a single slit of width 0.12mm is obtained with a blue green light of wavelength 500 nm. The angular separation between central maximum and second order secondary maximum of the diffraction pattern is

A proton is moving along negative X axis. If a uniform magnetic field is applied parallel to the positive Z axis, then choose the correct answer from the following options;
1. The proton will experience magnetic force along positive Y direction and will move along a circular path in the XY plane
2. The proton will experience magnetic force along negative Y direction and will move along a circular path in the XY plane
3. The proton will experience magnetic force along positive Y direction and will move along a circular path in the XZ plane
4. The proton will experience magnetic force along negative Y direction and will move along a circular path in the XZ plane

The negation of the proposition "If 2 is prime, then 3 is odd" is

If only \(2 \%\) of the main current is to be passed through a galvanometer of resistance \(G\), then the resistance of shunt should be

\(A+B \rightleftharpoons C+D\)
The initial concentrations of \(A\) and \(B\) are equal. At equilibrium, the concentration of \(C\) is twice that of \(A\). The equilibrium constant of the reaction is

The function \(f(x) = |x| + |x - 1|\) is:

A bulb of resistance 280 Ohm is supplied with a voltage \(\mathrm{V}=400 \sin \pi \mathrm{t}\). The peak current is